Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8011,2,Mod(1,8011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8011, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8011.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9681570592\) |
Analytic rank: | \(0\) |
Dimension: | \(358\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 8011.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.70980 | −1.91612 | −0.958061 | − | 0.286566i | \(-0.907486\pi\) | ||||
−0.958061 | + | 0.286566i | \(0.907486\pi\) | |||||||
\(3\) | −2.88951 | −1.66826 | −0.834131 | − | 0.551567i | \(-0.814030\pi\) | ||||
−0.834131 | + | 0.551567i | \(0.814030\pi\) | |||||||
\(4\) | 5.34304 | 2.67152 | ||||||||
\(5\) | −1.42877 | −0.638967 | −0.319484 | − | 0.947592i | \(-0.603509\pi\) | ||||
−0.319484 | + | 0.947592i | \(0.603509\pi\) | |||||||
\(6\) | 7.83002 | 3.19659 | ||||||||
\(7\) | −3.83323 | −1.44883 | −0.724413 | − | 0.689366i | \(-0.757889\pi\) | ||||
−0.724413 | + | 0.689366i | \(0.757889\pi\) | |||||||
\(8\) | −9.05899 | −3.20284 | ||||||||
\(9\) | 5.34929 | 1.78310 | ||||||||
\(10\) | 3.87170 | 1.22434 | ||||||||
\(11\) | −1.77195 | −0.534264 | −0.267132 | − | 0.963660i | \(-0.586076\pi\) | ||||
−0.267132 | + | 0.963660i | \(0.586076\pi\) | |||||||
\(12\) | −15.4388 | −4.45679 | ||||||||
\(13\) | −2.78462 | −0.772314 | −0.386157 | − | 0.922433i | \(-0.626198\pi\) | ||||
−0.386157 | + | 0.922433i | \(0.626198\pi\) | |||||||
\(14\) | 10.3873 | 2.77613 | ||||||||
\(15\) | 4.12846 | 1.06596 | ||||||||
\(16\) | 13.8620 | 3.46550 | ||||||||
\(17\) | 5.22233 | 1.26660 | 0.633301 | − | 0.773906i | \(-0.281700\pi\) | ||||
0.633301 | + | 0.773906i | \(0.281700\pi\) | |||||||
\(18\) | −14.4955 | −3.41663 | ||||||||
\(19\) | 1.32291 | 0.303496 | 0.151748 | − | 0.988419i | \(-0.451510\pi\) | ||||
0.151748 | + | 0.988419i | \(0.451510\pi\) | |||||||
\(20\) | −7.63400 | −1.70701 | ||||||||
\(21\) | 11.0762 | 2.41702 | ||||||||
\(22\) | 4.80165 | 1.02371 | ||||||||
\(23\) | −7.98809 | −1.66563 | −0.832816 | − | 0.553550i | \(-0.813273\pi\) | ||||
−0.832816 | + | 0.553550i | \(0.813273\pi\) | |||||||
\(24\) | 26.1761 | 5.34317 | ||||||||
\(25\) | −2.95860 | −0.591721 | ||||||||
\(26\) | 7.54577 | 1.47985 | ||||||||
\(27\) | −6.78830 | −1.30641 | ||||||||
\(28\) | −20.4811 | −3.87057 | ||||||||
\(29\) | 8.30704 | 1.54258 | 0.771290 | − | 0.636484i | \(-0.219612\pi\) | ||||
0.771290 | + | 0.636484i | \(0.219612\pi\) | |||||||
\(30\) | −11.1873 | −2.04252 | ||||||||
\(31\) | 4.90753 | 0.881418 | 0.440709 | − | 0.897650i | \(-0.354727\pi\) | ||||
0.440709 | + | 0.897650i | \(0.354727\pi\) | |||||||
\(32\) | −19.4454 | −3.43749 | ||||||||
\(33\) | 5.12008 | 0.891292 | ||||||||
\(34\) | −14.1515 | −2.42696 | ||||||||
\(35\) | 5.47683 | 0.925753 | ||||||||
\(36\) | 28.5815 | 4.76358 | ||||||||
\(37\) | 9.12496 | 1.50013 | 0.750067 | − | 0.661361i | \(-0.230021\pi\) | ||||
0.750067 | + | 0.661361i | \(0.230021\pi\) | |||||||
\(38\) | −3.58483 | −0.581536 | ||||||||
\(39\) | 8.04619 | 1.28842 | ||||||||
\(40\) | 12.9433 | 2.04651 | ||||||||
\(41\) | 11.9978 | 1.87374 | 0.936871 | − | 0.349675i | \(-0.113708\pi\) | ||||
0.936871 | + | 0.349675i | \(0.113708\pi\) | |||||||
\(42\) | −30.0143 | −4.63130 | ||||||||
\(43\) | −7.89656 | −1.20421 | −0.602107 | − | 0.798415i | \(-0.705672\pi\) | ||||
−0.602107 | + | 0.798415i | \(0.705672\pi\) | |||||||
\(44\) | −9.46762 | −1.42730 | ||||||||
\(45\) | −7.64293 | −1.13934 | ||||||||
\(46\) | 21.6462 | 3.19155 | ||||||||
\(47\) | −3.43126 | −0.500501 | −0.250250 | − | 0.968181i | \(-0.580513\pi\) | ||||
−0.250250 | + | 0.968181i | \(0.580513\pi\) | |||||||
\(48\) | −40.0545 | −5.78136 | ||||||||
\(49\) | 7.69368 | 1.09910 | ||||||||
\(50\) | 8.01724 | 1.13381 | ||||||||
\(51\) | −15.0900 | −2.11302 | ||||||||
\(52\) | −14.8783 | −2.06325 | ||||||||
\(53\) | 5.91825 | 0.812934 | 0.406467 | − | 0.913666i | \(-0.366761\pi\) | ||||
0.406467 | + | 0.913666i | \(0.366761\pi\) | |||||||
\(54\) | 18.3950 | 2.50324 | ||||||||
\(55\) | 2.53172 | 0.341377 | ||||||||
\(56\) | 34.7252 | 4.64035 | ||||||||
\(57\) | −3.82256 | −0.506311 | ||||||||
\(58\) | −22.5105 | −2.95577 | ||||||||
\(59\) | −0.635113 | −0.0826847 | −0.0413423 | − | 0.999145i | \(-0.513163\pi\) | ||||
−0.0413423 | + | 0.999145i | \(0.513163\pi\) | |||||||
\(60\) | 22.0586 | 2.84775 | ||||||||
\(61\) | −3.47084 | −0.444395 | −0.222198 | − | 0.975002i | \(-0.571323\pi\) | ||||
−0.222198 | + | 0.975002i | \(0.571323\pi\) | |||||||
\(62\) | −13.2984 | −1.68890 | ||||||||
\(63\) | −20.5051 | −2.58340 | ||||||||
\(64\) | 24.9691 | 3.12114 | ||||||||
\(65\) | 3.97859 | 0.493484 | ||||||||
\(66\) | −13.8744 | −1.70782 | ||||||||
\(67\) | −3.67411 | −0.448863 | −0.224432 | − | 0.974490i | \(-0.572053\pi\) | ||||
−0.224432 | + | 0.974490i | \(0.572053\pi\) | |||||||
\(68\) | 27.9031 | 3.38375 | ||||||||
\(69\) | 23.0817 | 2.77871 | ||||||||
\(70\) | −14.8411 | −1.77385 | ||||||||
\(71\) | 2.70307 | 0.320796 | 0.160398 | − | 0.987052i | \(-0.448722\pi\) | ||||
0.160398 | + | 0.987052i | \(0.448722\pi\) | |||||||
\(72\) | −48.4591 | −5.71096 | ||||||||
\(73\) | −2.67837 | −0.313479 | −0.156740 | − | 0.987640i | \(-0.550098\pi\) | ||||
−0.156740 | + | 0.987640i | \(0.550098\pi\) | |||||||
\(74\) | −24.7269 | −2.87444 | ||||||||
\(75\) | 8.54892 | 0.987144 | ||||||||
\(76\) | 7.06836 | 0.810796 | ||||||||
\(77\) | 6.79231 | 0.774056 | ||||||||
\(78\) | −21.8036 | −2.46877 | ||||||||
\(79\) | 9.08912 | 1.02261 | 0.511303 | − | 0.859400i | \(-0.329163\pi\) | ||||
0.511303 | + | 0.859400i | \(0.329163\pi\) | |||||||
\(80\) | −19.8057 | −2.21434 | ||||||||
\(81\) | 3.56701 | 0.396335 | ||||||||
\(82\) | −32.5117 | −3.59032 | ||||||||
\(83\) | 9.99796 | 1.09742 | 0.548709 | − | 0.836013i | \(-0.315119\pi\) | ||||
0.548709 | + | 0.836013i | \(0.315119\pi\) | |||||||
\(84\) | 59.1805 | 6.45712 | ||||||||
\(85\) | −7.46154 | −0.809317 | ||||||||
\(86\) | 21.3981 | 2.30742 | ||||||||
\(87\) | −24.0033 | −2.57342 | ||||||||
\(88\) | 16.0521 | 1.71116 | ||||||||
\(89\) | −16.7217 | −1.77250 | −0.886250 | − | 0.463207i | \(-0.846699\pi\) | ||||
−0.886250 | + | 0.463207i | \(0.846699\pi\) | |||||||
\(90\) | 20.7108 | 2.18311 | ||||||||
\(91\) | 10.6741 | 1.11895 | ||||||||
\(92\) | −42.6807 | −4.44977 | ||||||||
\(93\) | −14.1804 | −1.47044 | ||||||||
\(94\) | 9.29804 | 0.959020 | ||||||||
\(95\) | −1.89014 | −0.193924 | ||||||||
\(96\) | 56.1876 | 5.73462 | ||||||||
\(97\) | 10.2160 | 1.03728 | 0.518640 | − | 0.854992i | \(-0.326438\pi\) | ||||
0.518640 | + | 0.854992i | \(0.326438\pi\) | |||||||
\(98\) | −20.8484 | −2.10600 | ||||||||
\(99\) | −9.47869 | −0.952644 | ||||||||
\(100\) | −15.8079 | −1.58079 | ||||||||
\(101\) | −15.1185 | −1.50434 | −0.752172 | − | 0.658967i | \(-0.770994\pi\) | ||||
−0.752172 | + | 0.658967i | \(0.770994\pi\) | |||||||
\(102\) | 40.8909 | 4.04881 | ||||||||
\(103\) | 2.59956 | 0.256142 | 0.128071 | − | 0.991765i | \(-0.459121\pi\) | ||||
0.128071 | + | 0.991765i | \(0.459121\pi\) | |||||||
\(104\) | 25.2258 | 2.47360 | ||||||||
\(105\) | −15.8254 | −1.54440 | ||||||||
\(106\) | −16.0373 | −1.55768 | ||||||||
\(107\) | 15.3589 | 1.48480 | 0.742400 | − | 0.669956i | \(-0.233687\pi\) | ||||
0.742400 | + | 0.669956i | \(0.233687\pi\) | |||||||
\(108\) | −36.2701 | −3.49010 | ||||||||
\(109\) | −6.72982 | −0.644600 | −0.322300 | − | 0.946638i | \(-0.604456\pi\) | ||||
−0.322300 | + | 0.946638i | \(0.604456\pi\) | |||||||
\(110\) | −6.86047 | −0.654120 | ||||||||
\(111\) | −26.3667 | −2.50262 | ||||||||
\(112\) | −53.1363 | −5.02091 | ||||||||
\(113\) | 18.8419 | 1.77249 | 0.886247 | − | 0.463213i | \(-0.153304\pi\) | ||||
0.886247 | + | 0.463213i | \(0.153304\pi\) | |||||||
\(114\) | 10.3584 | 0.970153 | ||||||||
\(115\) | 11.4132 | 1.06428 | ||||||||
\(116\) | 44.3849 | 4.12103 | ||||||||
\(117\) | −14.8957 | −1.37711 | ||||||||
\(118\) | 1.72103 | 0.158434 | ||||||||
\(119\) | −20.0184 | −1.83509 | ||||||||
\(120\) | −37.3997 | −3.41411 | ||||||||
\(121\) | −7.86018 | −0.714562 | ||||||||
\(122\) | 9.40529 | 0.851515 | ||||||||
\(123\) | −34.6678 | −3.12589 | ||||||||
\(124\) | 26.2211 | 2.35473 | ||||||||
\(125\) | 11.3711 | 1.01706 | ||||||||
\(126\) | 55.5647 | 4.95010 | ||||||||
\(127\) | −10.5252 | −0.933961 | −0.466981 | − | 0.884268i | \(-0.654658\pi\) | ||||
−0.466981 | + | 0.884268i | \(0.654658\pi\) | |||||||
\(128\) | −28.7707 | −2.54299 | ||||||||
\(129\) | 22.8172 | 2.00894 | ||||||||
\(130\) | −10.7812 | −0.945575 | ||||||||
\(131\) | −1.53735 | −0.134319 | −0.0671594 | − | 0.997742i | \(-0.521394\pi\) | ||||
−0.0671594 | + | 0.997742i | \(0.521394\pi\) | |||||||
\(132\) | 27.3568 | 2.38110 | ||||||||
\(133\) | −5.07102 | −0.439713 | ||||||||
\(134\) | 9.95611 | 0.860077 | ||||||||
\(135\) | 9.69895 | 0.834752 | ||||||||
\(136\) | −47.3090 | −4.05672 | ||||||||
\(137\) | 1.27855 | 0.109234 | 0.0546169 | − | 0.998507i | \(-0.482606\pi\) | ||||
0.0546169 | + | 0.998507i | \(0.482606\pi\) | |||||||
\(138\) | −62.5469 | −5.32434 | ||||||||
\(139\) | −10.5073 | −0.891217 | −0.445609 | − | 0.895228i | \(-0.647013\pi\) | ||||
−0.445609 | + | 0.895228i | \(0.647013\pi\) | |||||||
\(140\) | 29.2629 | 2.47317 | ||||||||
\(141\) | 9.91467 | 0.834966 | ||||||||
\(142\) | −7.32480 | −0.614684 | ||||||||
\(143\) | 4.93421 | 0.412620 | ||||||||
\(144\) | 74.1519 | 6.17932 | ||||||||
\(145\) | −11.8689 | −0.985658 | ||||||||
\(146\) | 7.25786 | 0.600664 | ||||||||
\(147\) | −22.2310 | −1.83358 | ||||||||
\(148\) | 48.7551 | 4.00764 | ||||||||
\(149\) | 10.8544 | 0.889229 | 0.444614 | − | 0.895722i | \(-0.353341\pi\) | ||||
0.444614 | + | 0.895722i | \(0.353341\pi\) | |||||||
\(150\) | −23.1659 | −1.89149 | ||||||||
\(151\) | −8.07195 | −0.656886 | −0.328443 | − | 0.944524i | \(-0.606524\pi\) | ||||
−0.328443 | + | 0.944524i | \(0.606524\pi\) | |||||||
\(152\) | −11.9842 | −0.972049 | ||||||||
\(153\) | 27.9358 | 2.25847 | ||||||||
\(154\) | −18.4058 | −1.48318 | ||||||||
\(155\) | −7.01175 | −0.563197 | ||||||||
\(156\) | 42.9911 | 3.44205 | ||||||||
\(157\) | 23.6772 | 1.88964 | 0.944822 | − | 0.327583i | \(-0.106234\pi\) | ||||
0.944822 | + | 0.327583i | \(0.106234\pi\) | |||||||
\(158\) | −24.6297 | −1.95944 | ||||||||
\(159\) | −17.1009 | −1.35619 | ||||||||
\(160\) | 27.7830 | 2.19644 | ||||||||
\(161\) | 30.6202 | 2.41321 | ||||||||
\(162\) | −9.66590 | −0.759425 | ||||||||
\(163\) | 5.34506 | 0.418658 | 0.209329 | − | 0.977845i | \(-0.432872\pi\) | ||||
0.209329 | + | 0.977845i | \(0.432872\pi\) | |||||||
\(164\) | 64.1048 | 5.00574 | ||||||||
\(165\) | −7.31544 | −0.569507 | ||||||||
\(166\) | −27.0925 | −2.10279 | ||||||||
\(167\) | −4.26388 | −0.329949 | −0.164975 | − | 0.986298i | \(-0.552754\pi\) | ||||
−0.164975 | + | 0.986298i | \(0.552754\pi\) | |||||||
\(168\) | −100.339 | −7.74132 | ||||||||
\(169\) | −5.24590 | −0.403531 | ||||||||
\(170\) | 20.2193 | 1.55075 | ||||||||
\(171\) | 7.07662 | 0.541163 | ||||||||
\(172\) | −42.1917 | −3.21708 | ||||||||
\(173\) | 10.0473 | 0.763881 | 0.381941 | − | 0.924187i | \(-0.375256\pi\) | ||||
0.381941 | + | 0.924187i | \(0.375256\pi\) | |||||||
\(174\) | 65.0443 | 4.93099 | ||||||||
\(175\) | 11.3410 | 0.857300 | ||||||||
\(176\) | −24.5628 | −1.85149 | ||||||||
\(177\) | 1.83517 | 0.137940 | ||||||||
\(178\) | 45.3126 | 3.39633 | ||||||||
\(179\) | −18.7289 | −1.39986 | −0.699931 | − | 0.714210i | \(-0.746786\pi\) | ||||
−0.699931 | + | 0.714210i | \(0.746786\pi\) | |||||||
\(180\) | −40.8365 | −3.04377 | ||||||||
\(181\) | −22.8576 | −1.69899 | −0.849496 | − | 0.527595i | \(-0.823094\pi\) | ||||
−0.849496 | + | 0.527595i | \(0.823094\pi\) | |||||||
\(182\) | −28.9247 | −2.14404 | ||||||||
\(183\) | 10.0290 | 0.741368 | ||||||||
\(184\) | 72.3640 | 5.33475 | ||||||||
\(185\) | −13.0375 | −0.958537 | ||||||||
\(186\) | 38.4260 | 2.81753 | ||||||||
\(187\) | −9.25373 | −0.676700 | ||||||||
\(188\) | −18.3334 | −1.33710 | ||||||||
\(189\) | 26.0211 | 1.89276 | ||||||||
\(190\) | 5.12191 | 0.371582 | ||||||||
\(191\) | 11.1641 | 0.807804 | 0.403902 | − | 0.914802i | \(-0.367654\pi\) | ||||
0.403902 | + | 0.914802i | \(0.367654\pi\) | |||||||
\(192\) | −72.1485 | −5.20687 | ||||||||
\(193\) | 6.38782 | 0.459805 | 0.229903 | − | 0.973214i | \(-0.426159\pi\) | ||||
0.229903 | + | 0.973214i | \(0.426159\pi\) | |||||||
\(194\) | −27.6835 | −1.98756 | ||||||||
\(195\) | −11.4962 | −0.823260 | ||||||||
\(196\) | 41.1077 | 2.93626 | ||||||||
\(197\) | −13.1387 | −0.936096 | −0.468048 | − | 0.883703i | \(-0.655043\pi\) | ||||
−0.468048 | + | 0.883703i | \(0.655043\pi\) | |||||||
\(198\) | 25.6854 | 1.82538 | ||||||||
\(199\) | −7.96614 | −0.564705 | −0.282352 | − | 0.959311i | \(-0.591115\pi\) | ||||
−0.282352 | + | 0.959311i | \(0.591115\pi\) | |||||||
\(200\) | 26.8019 | 1.89518 | ||||||||
\(201\) | 10.6164 | 0.748821 | ||||||||
\(202\) | 40.9681 | 2.88251 | ||||||||
\(203\) | −31.8428 | −2.23493 | ||||||||
\(204\) | −80.6265 | −5.64498 | ||||||||
\(205\) | −17.1422 | −1.19726 | ||||||||
\(206\) | −7.04429 | −0.490799 | ||||||||
\(207\) | −42.7306 | −2.96998 | ||||||||
\(208\) | −38.6004 | −2.67646 | ||||||||
\(209\) | −2.34413 | −0.162147 | ||||||||
\(210\) | 42.8837 | 2.95925 | ||||||||
\(211\) | −10.6888 | −0.735850 | −0.367925 | − | 0.929855i | \(-0.619932\pi\) | ||||
−0.367925 | + | 0.929855i | \(0.619932\pi\) | |||||||
\(212\) | 31.6214 | 2.17177 | ||||||||
\(213\) | −7.81057 | −0.535171 | ||||||||
\(214\) | −41.6196 | −2.84506 | ||||||||
\(215\) | 11.2824 | 0.769454 | ||||||||
\(216\) | 61.4951 | 4.18421 | ||||||||
\(217\) | −18.8117 | −1.27702 | ||||||||
\(218\) | 18.2365 | 1.23513 | ||||||||
\(219\) | 7.73918 | 0.522965 | ||||||||
\(220\) | 13.5271 | 0.911997 | ||||||||
\(221\) | −14.5422 | −0.978214 | ||||||||
\(222\) | 71.4486 | 4.79532 | ||||||||
\(223\) | 12.2530 | 0.820519 | 0.410260 | − | 0.911969i | \(-0.365438\pi\) | ||||
0.410260 | + | 0.911969i | \(0.365438\pi\) | |||||||
\(224\) | 74.5386 | 4.98032 | ||||||||
\(225\) | −15.8264 | −1.05509 | ||||||||
\(226\) | −51.0578 | −3.39631 | ||||||||
\(227\) | −1.64371 | −0.109097 | −0.0545484 | − | 0.998511i | \(-0.517372\pi\) | ||||
−0.0545484 | + | 0.998511i | \(0.517372\pi\) | |||||||
\(228\) | −20.4241 | −1.35262 | ||||||||
\(229\) | 13.4902 | 0.891456 | 0.445728 | − | 0.895168i | \(-0.352945\pi\) | ||||
0.445728 | + | 0.895168i | \(0.352945\pi\) | |||||||
\(230\) | −30.9275 | −2.03930 | ||||||||
\(231\) | −19.6265 | −1.29133 | ||||||||
\(232\) | −75.2534 | −4.94063 | ||||||||
\(233\) | −9.84455 | −0.644938 | −0.322469 | − | 0.946580i | \(-0.604513\pi\) | ||||
−0.322469 | + | 0.946580i | \(0.604513\pi\) | |||||||
\(234\) | 40.3645 | 2.63871 | ||||||||
\(235\) | 4.90250 | 0.319804 | ||||||||
\(236\) | −3.39344 | −0.220894 | ||||||||
\(237\) | −26.2631 | −1.70597 | ||||||||
\(238\) | 54.2460 | 3.51625 | ||||||||
\(239\) | 12.0164 | 0.777279 | 0.388640 | − | 0.921390i | \(-0.372945\pi\) | ||||
0.388640 | + | 0.921390i | \(0.372945\pi\) | |||||||
\(240\) | 57.2288 | 3.69410 | ||||||||
\(241\) | 12.1346 | 0.781661 | 0.390830 | − | 0.920463i | \(-0.372188\pi\) | ||||
0.390830 | + | 0.920463i | \(0.372188\pi\) | |||||||
\(242\) | 21.2996 | 1.36919 | ||||||||
\(243\) | 10.0580 | 0.645219 | ||||||||
\(244\) | −18.5448 | −1.18721 | ||||||||
\(245\) | −10.9925 | −0.702288 | ||||||||
\(246\) | 93.9430 | 5.98959 | ||||||||
\(247\) | −3.68380 | −0.234394 | ||||||||
\(248\) | −44.4572 | −2.82304 | ||||||||
\(249\) | −28.8892 | −1.83078 | ||||||||
\(250\) | −30.8133 | −1.94881 | ||||||||
\(251\) | 19.6871 | 1.24264 | 0.621318 | − | 0.783559i | \(-0.286598\pi\) | ||||
0.621318 | + | 0.783559i | \(0.286598\pi\) | |||||||
\(252\) | −109.559 | −6.90160 | ||||||||
\(253\) | 14.1545 | 0.889887 | ||||||||
\(254\) | 28.5213 | 1.78958 | ||||||||
\(255\) | 21.5602 | 1.35015 | ||||||||
\(256\) | 28.0247 | 1.75154 | ||||||||
\(257\) | 20.9205 | 1.30498 | 0.652492 | − | 0.757796i | \(-0.273724\pi\) | ||||
0.652492 | + | 0.757796i | \(0.273724\pi\) | |||||||
\(258\) | −61.8302 | −3.84938 | ||||||||
\(259\) | −34.9781 | −2.17343 | ||||||||
\(260\) | 21.2578 | 1.31835 | ||||||||
\(261\) | 44.4368 | 2.75057 | ||||||||
\(262\) | 4.16591 | 0.257371 | ||||||||
\(263\) | 23.3252 | 1.43829 | 0.719147 | − | 0.694858i | \(-0.244533\pi\) | ||||
0.719147 | + | 0.694858i | \(0.244533\pi\) | |||||||
\(264\) | −46.3828 | −2.85466 | ||||||||
\(265\) | −8.45584 | −0.519438 | ||||||||
\(266\) | 13.7415 | 0.842544 | ||||||||
\(267\) | 48.3177 | 2.95699 | ||||||||
\(268\) | −19.6309 | −1.19915 | ||||||||
\(269\) | 21.1677 | 1.29062 | 0.645309 | − | 0.763922i | \(-0.276729\pi\) | ||||
0.645309 | + | 0.763922i | \(0.276729\pi\) | |||||||
\(270\) | −26.2823 | −1.59949 | ||||||||
\(271\) | −16.4478 | −0.999132 | −0.499566 | − | 0.866276i | \(-0.666507\pi\) | ||||
−0.499566 | + | 0.866276i | \(0.666507\pi\) | |||||||
\(272\) | 72.3920 | 4.38941 | ||||||||
\(273\) | −30.8429 | −1.86670 | ||||||||
\(274\) | −3.46462 | −0.209305 | ||||||||
\(275\) | 5.24251 | 0.316135 | ||||||||
\(276\) | 123.326 | 7.42338 | ||||||||
\(277\) | −9.92574 | −0.596380 | −0.298190 | − | 0.954507i | \(-0.596383\pi\) | ||||
−0.298190 | + | 0.954507i | \(0.596383\pi\) | |||||||
\(278\) | 28.4727 | 1.70768 | ||||||||
\(279\) | 26.2518 | 1.57165 | ||||||||
\(280\) | −49.6145 | −2.96503 | ||||||||
\(281\) | −26.1765 | −1.56156 | −0.780779 | − | 0.624808i | \(-0.785177\pi\) | ||||
−0.780779 | + | 0.624808i | \(0.785177\pi\) | |||||||
\(282\) | −26.8668 | −1.59990 | ||||||||
\(283\) | −25.3553 | −1.50722 | −0.753608 | − | 0.657324i | \(-0.771688\pi\) | ||||
−0.753608 | + | 0.657324i | \(0.771688\pi\) | |||||||
\(284\) | 14.4426 | 0.857013 | ||||||||
\(285\) | 5.46158 | 0.323516 | ||||||||
\(286\) | −13.3708 | −0.790629 | ||||||||
\(287\) | −45.9904 | −2.71473 | ||||||||
\(288\) | −104.019 | −6.12937 | ||||||||
\(289\) | 10.2727 | 0.604279 | ||||||||
\(290\) | 32.1624 | 1.88864 | ||||||||
\(291\) | −29.5194 | −1.73046 | ||||||||
\(292\) | −14.3106 | −0.837466 | ||||||||
\(293\) | 4.49282 | 0.262474 | 0.131237 | − | 0.991351i | \(-0.458105\pi\) | ||||
0.131237 | + | 0.991351i | \(0.458105\pi\) | |||||||
\(294\) | 60.2417 | 3.51337 | ||||||||
\(295\) | 0.907434 | 0.0528328 | ||||||||
\(296\) | −82.6629 | −4.80469 | ||||||||
\(297\) | 12.0285 | 0.697967 | ||||||||
\(298\) | −29.4134 | −1.70387 | ||||||||
\(299\) | 22.2438 | 1.28639 | ||||||||
\(300\) | 45.6772 | 2.63718 | ||||||||
\(301\) | 30.2694 | 1.74470 | ||||||||
\(302\) | 21.8734 | 1.25867 | ||||||||
\(303\) | 43.6850 | 2.50964 | ||||||||
\(304\) | 18.3382 | 1.05177 | ||||||||
\(305\) | 4.95905 | 0.283954 | ||||||||
\(306\) | −75.7004 | −4.32751 | ||||||||
\(307\) | −5.42538 | −0.309643 | −0.154821 | − | 0.987942i | \(-0.549480\pi\) | ||||
−0.154821 | + | 0.987942i | \(0.549480\pi\) | |||||||
\(308\) | 36.2916 | 2.06791 | ||||||||
\(309\) | −7.51146 | −0.427312 | ||||||||
\(310\) | 19.0005 | 1.07915 | ||||||||
\(311\) | −23.7292 | −1.34556 | −0.672781 | − | 0.739842i | \(-0.734900\pi\) | ||||
−0.672781 | + | 0.739842i | \(0.734900\pi\) | |||||||
\(312\) | −72.8904 | −4.12660 | ||||||||
\(313\) | −20.8533 | −1.17870 | −0.589349 | − | 0.807879i | \(-0.700616\pi\) | ||||
−0.589349 | + | 0.807879i | \(0.700616\pi\) | |||||||
\(314\) | −64.1605 | −3.62079 | ||||||||
\(315\) | 29.2971 | 1.65071 | ||||||||
\(316\) | 48.5636 | 2.73191 | ||||||||
\(317\) | −28.0023 | −1.57277 | −0.786383 | − | 0.617739i | \(-0.788049\pi\) | ||||
−0.786383 | + | 0.617739i | \(0.788049\pi\) | |||||||
\(318\) | 46.3400 | 2.59862 | ||||||||
\(319\) | −14.7197 | −0.824145 | ||||||||
\(320\) | −35.6752 | −1.99431 | ||||||||
\(321\) | −44.3797 | −2.47704 | ||||||||
\(322\) | −82.9748 | −4.62401 | ||||||||
\(323\) | 6.90867 | 0.384409 | ||||||||
\(324\) | 19.0587 | 1.05882 | ||||||||
\(325\) | 8.23858 | 0.456994 | ||||||||
\(326\) | −14.4841 | −0.802199 | ||||||||
\(327\) | 19.4459 | 1.07536 | ||||||||
\(328\) | −108.688 | −6.00129 | ||||||||
\(329\) | 13.1528 | 0.725138 | ||||||||
\(330\) | 19.8234 | 1.09124 | ||||||||
\(331\) | −27.0060 | −1.48438 | −0.742192 | − | 0.670187i | \(-0.766214\pi\) | ||||
−0.742192 | + | 0.670187i | \(0.766214\pi\) | |||||||
\(332\) | 53.4195 | 2.93178 | ||||||||
\(333\) | 48.8121 | 2.67488 | ||||||||
\(334\) | 11.5543 | 0.632223 | ||||||||
\(335\) | 5.24947 | 0.286809 | ||||||||
\(336\) | 153.538 | 8.37619 | ||||||||
\(337\) | −0.285512 | −0.0155528 | −0.00777641 | − | 0.999970i | \(-0.502475\pi\) | ||||
−0.00777641 | + | 0.999970i | \(0.502475\pi\) | |||||||
\(338\) | 14.2154 | 0.773214 | ||||||||
\(339\) | −54.4438 | −2.95698 | ||||||||
\(340\) | −39.8673 | −2.16211 | ||||||||
\(341\) | −8.69591 | −0.470910 | ||||||||
\(342\) | −19.1763 | −1.03693 | ||||||||
\(343\) | −2.65905 | −0.143575 | ||||||||
\(344\) | 71.5349 | 3.85690 | ||||||||
\(345\) | −32.9785 | −1.77551 | ||||||||
\(346\) | −27.2262 | −1.46369 | ||||||||
\(347\) | −12.5188 | −0.672046 | −0.336023 | − | 0.941854i | \(-0.609082\pi\) | ||||
−0.336023 | + | 0.941854i | \(0.609082\pi\) | |||||||
\(348\) | −128.251 | −6.87496 | ||||||||
\(349\) | −17.1667 | −0.918912 | −0.459456 | − | 0.888200i | \(-0.651956\pi\) | ||||
−0.459456 | + | 0.888200i | \(0.651956\pi\) | |||||||
\(350\) | −30.7319 | −1.64269 | ||||||||
\(351\) | 18.9028 | 1.00896 | ||||||||
\(352\) | 34.4563 | 1.83652 | ||||||||
\(353\) | −29.8553 | −1.58904 | −0.794520 | − | 0.607238i | \(-0.792277\pi\) | ||||
−0.794520 | + | 0.607238i | \(0.792277\pi\) | |||||||
\(354\) | −4.97295 | −0.264309 | ||||||||
\(355\) | −3.86208 | −0.204978 | ||||||||
\(356\) | −89.3449 | −4.73527 | ||||||||
\(357\) | 57.8435 | 3.06140 | ||||||||
\(358\) | 50.7516 | 2.68231 | ||||||||
\(359\) | −4.71127 | −0.248651 | −0.124326 | − | 0.992241i | \(-0.539677\pi\) | ||||
−0.124326 | + | 0.992241i | \(0.539677\pi\) | |||||||
\(360\) | 69.2372 | 3.64912 | ||||||||
\(361\) | −17.2499 | −0.907890 | ||||||||
\(362\) | 61.9396 | 3.25547 | ||||||||
\(363\) | 22.7121 | 1.19208 | ||||||||
\(364\) | 57.0321 | 2.98930 | ||||||||
\(365\) | 3.82679 | 0.200303 | ||||||||
\(366\) | −27.1767 | −1.42055 | ||||||||
\(367\) | 6.67163 | 0.348256 | 0.174128 | − | 0.984723i | \(-0.444289\pi\) | ||||
0.174128 | + | 0.984723i | \(0.444289\pi\) | |||||||
\(368\) | −110.731 | −5.77225 | ||||||||
\(369\) | 64.1797 | 3.34106 | ||||||||
\(370\) | 35.3291 | 1.83667 | ||||||||
\(371\) | −22.6860 | −1.17780 | ||||||||
\(372\) | −75.7663 | −3.92830 | ||||||||
\(373\) | 17.9752 | 0.930723 | 0.465362 | − | 0.885121i | \(-0.345924\pi\) | ||||
0.465362 | + | 0.885121i | \(0.345924\pi\) | |||||||
\(374\) | 25.0758 | 1.29664 | ||||||||
\(375\) | −32.8568 | −1.69672 | ||||||||
\(376\) | 31.0837 | 1.60302 | ||||||||
\(377\) | −23.1319 | −1.19136 | ||||||||
\(378\) | −70.5122 | −3.62675 | ||||||||
\(379\) | −22.2881 | −1.14486 | −0.572432 | − | 0.819952i | \(-0.694000\pi\) | ||||
−0.572432 | + | 0.819952i | \(0.694000\pi\) | |||||||
\(380\) | −10.0991 | −0.518073 | ||||||||
\(381\) | 30.4127 | 1.55809 | ||||||||
\(382\) | −30.2524 | −1.54785 | ||||||||
\(383\) | −24.0199 | −1.22736 | −0.613680 | − | 0.789555i | \(-0.710311\pi\) | ||||
−0.613680 | + | 0.789555i | \(0.710311\pi\) | |||||||
\(384\) | 83.1332 | 4.24237 | ||||||||
\(385\) | −9.70468 | −0.494596 | ||||||||
\(386\) | −17.3097 | −0.881043 | ||||||||
\(387\) | −42.2410 | −2.14723 | ||||||||
\(388\) | 54.5847 | 2.77112 | ||||||||
\(389\) | 24.3599 | 1.23510 | 0.617548 | − | 0.786533i | \(-0.288126\pi\) | ||||
0.617548 | + | 0.786533i | \(0.288126\pi\) | |||||||
\(390\) | 31.1524 | 1.57747 | ||||||||
\(391\) | −41.7165 | −2.10969 | ||||||||
\(392\) | −69.6970 | −3.52023 | ||||||||
\(393\) | 4.44219 | 0.224079 | ||||||||
\(394\) | 35.6034 | 1.79367 | ||||||||
\(395\) | −12.9863 | −0.653412 | ||||||||
\(396\) | −50.6450 | −2.54501 | ||||||||
\(397\) | −18.6209 | −0.934558 | −0.467279 | − | 0.884110i | \(-0.654766\pi\) | ||||
−0.467279 | + | 0.884110i | \(0.654766\pi\) | |||||||
\(398\) | 21.5867 | 1.08204 | ||||||||
\(399\) | 14.6528 | 0.733557 | ||||||||
\(400\) | −41.0122 | −2.05061 | ||||||||
\(401\) | −15.9682 | −0.797413 | −0.398706 | − | 0.917079i | \(-0.630541\pi\) | ||||
−0.398706 | + | 0.917079i | \(0.630541\pi\) | |||||||
\(402\) | −28.7683 | −1.43483 | ||||||||
\(403\) | −13.6656 | −0.680732 | ||||||||
\(404\) | −80.7786 | −4.01889 | ||||||||
\(405\) | −5.09646 | −0.253245 | ||||||||
\(406\) | 86.2879 | 4.28239 | ||||||||
\(407\) | −16.1690 | −0.801468 | ||||||||
\(408\) | 136.700 | 6.76766 | ||||||||
\(409\) | 4.77904 | 0.236308 | 0.118154 | − | 0.992995i | \(-0.462302\pi\) | ||||
0.118154 | + | 0.992995i | \(0.462302\pi\) | |||||||
\(410\) | 46.4519 | 2.29410 | ||||||||
\(411\) | −3.69438 | −0.182230 | ||||||||
\(412\) | 13.8895 | 0.684289 | ||||||||
\(413\) | 2.43454 | 0.119796 | ||||||||
\(414\) | 115.792 | 5.69084 | ||||||||
\(415\) | −14.2848 | −0.701215 | ||||||||
\(416\) | 54.1479 | 2.65482 | ||||||||
\(417\) | 30.3610 | 1.48678 | ||||||||
\(418\) | 6.35214 | 0.310694 | ||||||||
\(419\) | 16.1191 | 0.787468 | 0.393734 | − | 0.919224i | \(-0.371183\pi\) | ||||
0.393734 | + | 0.919224i | \(0.371183\pi\) | |||||||
\(420\) | −84.5556 | −4.12589 | ||||||||
\(421\) | 1.45900 | 0.0711072 | 0.0355536 | − | 0.999368i | \(-0.488681\pi\) | ||||
0.0355536 | + | 0.999368i | \(0.488681\pi\) | |||||||
\(422\) | 28.9647 | 1.40998 | ||||||||
\(423\) | −18.3548 | −0.892440 | ||||||||
\(424\) | −53.6133 | −2.60369 | ||||||||
\(425\) | −15.4508 | −0.749474 | ||||||||
\(426\) | 21.1651 | 1.02545 | ||||||||
\(427\) | 13.3045 | 0.643852 | ||||||||
\(428\) | 82.0632 | 3.96668 | ||||||||
\(429\) | −14.2575 | −0.688357 | ||||||||
\(430\) | −30.5731 | −1.47437 | ||||||||
\(431\) | −15.2265 | −0.733433 | −0.366717 | − | 0.930333i | \(-0.619518\pi\) | ||||
−0.366717 | + | 0.930333i | \(0.619518\pi\) | |||||||
\(432\) | −94.0994 | −4.52736 | ||||||||
\(433\) | −25.2105 | −1.21154 | −0.605769 | − | 0.795641i | \(-0.707134\pi\) | ||||
−0.605769 | + | 0.795641i | \(0.707134\pi\) | |||||||
\(434\) | 50.9760 | 2.44693 | ||||||||
\(435\) | 34.2953 | 1.64433 | ||||||||
\(436\) | −35.9577 | −1.72206 | ||||||||
\(437\) | −10.5675 | −0.505513 | ||||||||
\(438\) | −20.9717 | −1.00207 | ||||||||
\(439\) | −13.0209 | −0.621455 | −0.310727 | − | 0.950499i | \(-0.600573\pi\) | ||||
−0.310727 | + | 0.950499i | \(0.600573\pi\) | |||||||
\(440\) | −22.9348 | −1.09338 | ||||||||
\(441\) | 41.1557 | 1.95980 | ||||||||
\(442\) | 39.4065 | 1.87438 | ||||||||
\(443\) | 8.69065 | 0.412905 | 0.206453 | − | 0.978457i | \(-0.433808\pi\) | ||||
0.206453 | + | 0.978457i | \(0.433808\pi\) | |||||||
\(444\) | −140.878 | −6.68579 | ||||||||
\(445\) | 23.8916 | 1.13257 | ||||||||
\(446\) | −33.2031 | −1.57221 | ||||||||
\(447\) | −31.3640 | −1.48347 | ||||||||
\(448\) | −95.7124 | −4.52199 | ||||||||
\(449\) | −6.14292 | −0.289902 | −0.144951 | − | 0.989439i | \(-0.546303\pi\) | ||||
−0.144951 | + | 0.989439i | \(0.546303\pi\) | |||||||
\(450\) | 42.8865 | 2.02169 | ||||||||
\(451\) | −21.2595 | −1.00107 | ||||||||
\(452\) | 100.673 | 4.73525 | ||||||||
\(453\) | 23.3240 | 1.09586 | ||||||||
\(454\) | 4.45413 | 0.209043 | ||||||||
\(455\) | −15.2509 | −0.714972 | ||||||||
\(456\) | 34.6286 | 1.62163 | ||||||||
\(457\) | −5.64994 | −0.264293 | −0.132147 | − | 0.991230i | \(-0.542187\pi\) | ||||
−0.132147 | + | 0.991230i | \(0.542187\pi\) | |||||||
\(458\) | −36.5558 | −1.70814 | ||||||||
\(459\) | −35.4507 | −1.65470 | ||||||||
\(460\) | 60.9811 | 2.84326 | ||||||||
\(461\) | −34.9341 | −1.62704 | −0.813522 | − | 0.581534i | \(-0.802453\pi\) | ||||
−0.813522 | + | 0.581534i | \(0.802453\pi\) | |||||||
\(462\) | 53.1839 | 2.47434 | ||||||||
\(463\) | −5.10015 | −0.237024 | −0.118512 | − | 0.992953i | \(-0.537812\pi\) | ||||
−0.118512 | + | 0.992953i | \(0.537812\pi\) | |||||||
\(464\) | 115.152 | 5.34581 | ||||||||
\(465\) | 20.2605 | 0.939560 | ||||||||
\(466\) | 26.6768 | 1.23578 | ||||||||
\(467\) | 18.7010 | 0.865380 | 0.432690 | − | 0.901543i | \(-0.357565\pi\) | ||||
0.432690 | + | 0.901543i | \(0.357565\pi\) | |||||||
\(468\) | −79.5885 | −3.67898 | ||||||||
\(469\) | 14.0837 | 0.650325 | ||||||||
\(470\) | −13.2848 | −0.612782 | ||||||||
\(471\) | −68.4155 | −3.15242 | ||||||||
\(472\) | 5.75348 | 0.264826 | ||||||||
\(473\) | 13.9923 | 0.643369 | ||||||||
\(474\) | 71.1680 | 3.26885 | ||||||||
\(475\) | −3.91396 | −0.179585 | ||||||||
\(476\) | −106.959 | −4.90247 | ||||||||
\(477\) | 31.6584 | 1.44954 | ||||||||
\(478\) | −32.5622 | −1.48936 | ||||||||
\(479\) | 32.1391 | 1.46847 | 0.734237 | − | 0.678894i | \(-0.237540\pi\) | ||||
0.734237 | + | 0.678894i | \(0.237540\pi\) | |||||||
\(480\) | −80.2794 | −3.66424 | ||||||||
\(481\) | −25.4095 | −1.15858 | ||||||||
\(482\) | −32.8825 | −1.49776 | ||||||||
\(483\) | −88.4775 | −4.02587 | ||||||||
\(484\) | −41.9973 | −1.90897 | ||||||||
\(485\) | −14.5964 | −0.662789 | ||||||||
\(486\) | −27.2551 | −1.23632 | ||||||||
\(487\) | −35.7644 | −1.62064 | −0.810320 | − | 0.585988i | \(-0.800706\pi\) | ||||
−0.810320 | + | 0.585988i | \(0.800706\pi\) | |||||||
\(488\) | 31.4423 | 1.42333 | ||||||||
\(489\) | −15.4446 | −0.698430 | ||||||||
\(490\) | 29.7876 | 1.34567 | ||||||||
\(491\) | 26.6334 | 1.20195 | 0.600973 | − | 0.799269i | \(-0.294780\pi\) | ||||
0.600973 | + | 0.799269i | \(0.294780\pi\) | |||||||
\(492\) | −185.232 | −8.35088 | ||||||||
\(493\) | 43.3821 | 1.95383 | ||||||||
\(494\) | 9.98237 | 0.449128 | ||||||||
\(495\) | 13.5429 | 0.608708 | ||||||||
\(496\) | 68.0282 | 3.05456 | ||||||||
\(497\) | −10.3615 | −0.464777 | ||||||||
\(498\) | 78.2842 | 3.50800 | ||||||||
\(499\) | −11.7764 | −0.527183 | −0.263592 | − | 0.964634i | \(-0.584907\pi\) | ||||
−0.263592 | + | 0.964634i | \(0.584907\pi\) | |||||||
\(500\) | 60.7560 | 2.71709 | ||||||||
\(501\) | 12.3205 | 0.550441 | ||||||||
\(502\) | −53.3481 | −2.38104 | ||||||||
\(503\) | 7.25854 | 0.323642 | 0.161821 | − | 0.986820i | \(-0.448263\pi\) | ||||
0.161821 | + | 0.986820i | \(0.448263\pi\) | |||||||
\(504\) | 185.755 | 8.27419 | ||||||||
\(505\) | 21.6009 | 0.961227 | ||||||||
\(506\) | −38.3560 | −1.70513 | ||||||||
\(507\) | 15.1581 | 0.673195 | ||||||||
\(508\) | −56.2366 | −2.49510 | ||||||||
\(509\) | 30.6817 | 1.35994 | 0.679971 | − | 0.733239i | \(-0.261992\pi\) | ||||
0.679971 | + | 0.733239i | \(0.261992\pi\) | |||||||
\(510\) | −58.4239 | −2.58706 | ||||||||
\(511\) | 10.2668 | 0.454177 | ||||||||
\(512\) | −18.4001 | −0.813177 | ||||||||
\(513\) | −8.98030 | −0.396490 | ||||||||
\(514\) | −56.6904 | −2.50051 | ||||||||
\(515\) | −3.71418 | −0.163666 | ||||||||
\(516\) | 121.913 | 5.36694 | ||||||||
\(517\) | 6.08003 | 0.267399 | ||||||||
\(518\) | 94.7839 | 4.16456 | ||||||||
\(519\) | −29.0318 | −1.27435 | ||||||||
\(520\) | −36.0420 | −1.58055 | ||||||||
\(521\) | 0.510460 | 0.0223636 | 0.0111818 | − | 0.999937i | \(-0.496441\pi\) | ||||
0.0111818 | + | 0.999937i | \(0.496441\pi\) | |||||||
\(522\) | −120.415 | −5.27042 | ||||||||
\(523\) | 27.1358 | 1.18657 | 0.593283 | − | 0.804994i | \(-0.297832\pi\) | ||||
0.593283 | + | 0.804994i | \(0.297832\pi\) | |||||||
\(524\) | −8.21411 | −0.358835 | ||||||||
\(525\) | −32.7700 | −1.43020 | ||||||||
\(526\) | −63.2068 | −2.75595 | ||||||||
\(527\) | 25.6287 | 1.11641 | ||||||||
\(528\) | 70.9746 | 3.08877 | ||||||||
\(529\) | 40.8096 | 1.77433 | ||||||||
\(530\) | 22.9137 | 0.995307 | ||||||||
\(531\) | −3.39740 | −0.147435 | ||||||||
\(532\) | −27.0947 | −1.17470 | ||||||||
\(533\) | −33.4093 | −1.44712 | ||||||||
\(534\) | −130.931 | −5.66596 | ||||||||
\(535\) | −21.9444 | −0.948739 | ||||||||
\(536\) | 33.2837 | 1.43764 | ||||||||
\(537\) | 54.1174 | 2.33534 | ||||||||
\(538\) | −57.3603 | −2.47298 | ||||||||
\(539\) | −13.6328 | −0.587208 | ||||||||
\(540\) | 51.8219 | 2.23006 | ||||||||
\(541\) | 41.8205 | 1.79800 | 0.899002 | − | 0.437945i | \(-0.144294\pi\) | ||||
0.899002 | + | 0.437945i | \(0.144294\pi\) | |||||||
\(542\) | 44.5703 | 1.91446 | ||||||||
\(543\) | 66.0473 | 2.83436 | ||||||||
\(544\) | −101.550 | −4.35392 | ||||||||
\(545\) | 9.61540 | 0.411878 | ||||||||
\(546\) | 83.5783 | 3.57682 | ||||||||
\(547\) | −13.6772 | −0.584797 | −0.292398 | − | 0.956297i | \(-0.594453\pi\) | ||||
−0.292398 | + | 0.956297i | \(0.594453\pi\) | |||||||
\(548\) | 6.83134 | 0.291820 | ||||||||
\(549\) | −18.5665 | −0.792399 | ||||||||
\(550\) | −14.2062 | −0.605753 | ||||||||
\(551\) | 10.9895 | 0.468167 | ||||||||
\(552\) | −209.097 | −8.89975 | ||||||||
\(553\) | −34.8407 | −1.48158 | ||||||||
\(554\) | 26.8968 | 1.14274 | ||||||||
\(555\) | 37.6721 | 1.59909 | ||||||||
\(556\) | −56.1409 | −2.38091 | ||||||||
\(557\) | −43.6478 | −1.84942 | −0.924709 | − | 0.380675i | \(-0.875692\pi\) | ||||
−0.924709 | + | 0.380675i | \(0.875692\pi\) | |||||||
\(558\) | −71.1372 | −3.01148 | ||||||||
\(559\) | 21.9889 | 0.930032 | ||||||||
\(560\) | 75.9198 | 3.20820 | ||||||||
\(561\) | 26.7388 | 1.12891 | ||||||||
\(562\) | 70.9331 | 2.99213 | ||||||||
\(563\) | 33.9721 | 1.43175 | 0.715876 | − | 0.698227i | \(-0.246027\pi\) | ||||
0.715876 | + | 0.698227i | \(0.246027\pi\) | |||||||
\(564\) | 52.9745 | 2.23063 | ||||||||
\(565\) | −26.9208 | −1.13257 | ||||||||
\(566\) | 68.7079 | 2.88801 | ||||||||
\(567\) | −13.6732 | −0.574220 | ||||||||
\(568\) | −24.4871 | −1.02746 | ||||||||
\(569\) | 3.86187 | 0.161898 | 0.0809491 | − | 0.996718i | \(-0.474205\pi\) | ||||
0.0809491 | + | 0.996718i | \(0.474205\pi\) | |||||||
\(570\) | −14.7998 | −0.619896 | ||||||||
\(571\) | −18.2804 | −0.765010 | −0.382505 | − | 0.923954i | \(-0.624938\pi\) | ||||
−0.382505 | + | 0.923954i | \(0.624938\pi\) | |||||||
\(572\) | 26.3637 | 1.10232 | ||||||||
\(573\) | −32.2587 | −1.34763 | ||||||||
\(574\) | 124.625 | 5.20175 | ||||||||
\(575\) | 23.6336 | 0.985589 | ||||||||
\(576\) | 133.567 | 5.56529 | ||||||||
\(577\) | −23.1337 | −0.963069 | −0.481534 | − | 0.876427i | \(-0.659920\pi\) | ||||
−0.481534 | + | 0.876427i | \(0.659920\pi\) | |||||||
\(578\) | −27.8371 | −1.15787 | ||||||||
\(579\) | −18.4577 | −0.767075 | ||||||||
\(580\) | −63.4160 | −2.63321 | ||||||||
\(581\) | −38.3245 | −1.58997 | ||||||||
\(582\) | 79.9917 | 3.31576 | ||||||||
\(583\) | −10.4869 | −0.434321 | ||||||||
\(584\) | 24.2633 | 1.00402 | ||||||||
\(585\) | 21.2826 | 0.879929 | ||||||||
\(586\) | −12.1747 | −0.502931 | ||||||||
\(587\) | 28.5251 | 1.17736 | 0.588679 | − | 0.808367i | \(-0.299648\pi\) | ||||
0.588679 | + | 0.808367i | \(0.299648\pi\) | |||||||
\(588\) | −118.781 | −4.89845 | ||||||||
\(589\) | 6.49221 | 0.267507 | ||||||||
\(590\) | −2.45897 | −0.101234 | ||||||||
\(591\) | 37.9646 | 1.56165 | ||||||||
\(592\) | 126.490 | 5.19872 | ||||||||
\(593\) | −36.8277 | −1.51233 | −0.756166 | − | 0.654380i | \(-0.772930\pi\) | ||||
−0.756166 | + | 0.654380i | \(0.772930\pi\) | |||||||
\(594\) | −32.5950 | −1.33739 | ||||||||
\(595\) | 28.6018 | 1.17256 | ||||||||
\(596\) | 57.9956 | 2.37559 | ||||||||
\(597\) | 23.0183 | 0.942075 | ||||||||
\(598\) | −60.2763 | −2.46488 | ||||||||
\(599\) | −29.1279 | −1.19013 | −0.595067 | − | 0.803676i | \(-0.702874\pi\) | ||||
−0.595067 | + | 0.803676i | \(0.702874\pi\) | |||||||
\(600\) | −77.4446 | −3.16166 | ||||||||
\(601\) | 35.4979 | 1.44799 | 0.723994 | − | 0.689806i | \(-0.242304\pi\) | ||||
0.723994 | + | 0.689806i | \(0.242304\pi\) | |||||||
\(602\) | −82.0241 | −3.34305 | ||||||||
\(603\) | −19.6538 | −0.800366 | ||||||||
\(604\) | −43.1288 | −1.75489 | ||||||||
\(605\) | 11.2304 | 0.456582 | ||||||||
\(606\) | −118.378 | −4.80877 | ||||||||
\(607\) | 41.2155 | 1.67288 | 0.836442 | − | 0.548056i | \(-0.184632\pi\) | ||||
0.836442 | + | 0.548056i | \(0.184632\pi\) | |||||||
\(608\) | −25.7244 | −1.04326 | ||||||||
\(609\) | 92.0103 | 3.72845 | ||||||||
\(610\) | −13.4380 | −0.544091 | ||||||||
\(611\) | 9.55475 | 0.386544 | ||||||||
\(612\) | 149.262 | 6.03355 | ||||||||
\(613\) | 32.0359 | 1.29392 | 0.646960 | − | 0.762524i | \(-0.276040\pi\) | ||||
0.646960 | + | 0.762524i | \(0.276040\pi\) | |||||||
\(614\) | 14.7017 | 0.593313 | ||||||||
\(615\) | 49.5325 | 1.99734 | ||||||||
\(616\) | −61.5315 | −2.47917 | ||||||||
\(617\) | 18.5640 | 0.747358 | 0.373679 | − | 0.927558i | \(-0.378096\pi\) | ||||
0.373679 | + | 0.927558i | \(0.378096\pi\) | |||||||
\(618\) | 20.3546 | 0.818781 | ||||||||
\(619\) | 13.1283 | 0.527672 | 0.263836 | − | 0.964568i | \(-0.415012\pi\) | ||||
0.263836 | + | 0.964568i | \(0.415012\pi\) | |||||||
\(620\) | −37.4641 | −1.50459 | ||||||||
\(621\) | 54.2255 | 2.17600 | ||||||||
\(622\) | 64.3016 | 2.57826 | ||||||||
\(623\) | 64.0983 | 2.56804 | ||||||||
\(624\) | 111.536 | 4.46503 | ||||||||
\(625\) | −1.45366 | −0.0581463 | ||||||||
\(626\) | 56.5083 | 2.25853 | ||||||||
\(627\) | 6.77341 | 0.270504 | ||||||||
\(628\) | 126.508 | 5.04822 | ||||||||
\(629\) | 47.6536 | 1.90007 | ||||||||
\(630\) | −79.3895 | −3.16295 | ||||||||
\(631\) | −0.843975 | −0.0335981 | −0.0167991 | − | 0.999859i | \(-0.505348\pi\) | ||||
−0.0167991 | + | 0.999859i | \(0.505348\pi\) | |||||||
\(632\) | −82.3382 | −3.27524 | ||||||||
\(633\) | 30.8856 | 1.22759 | ||||||||
\(634\) | 75.8808 | 3.01361 | ||||||||
\(635\) | 15.0382 | 0.596771 | ||||||||
\(636\) | −91.3706 | −3.62308 | ||||||||
\(637\) | −21.4240 | −0.848849 | ||||||||
\(638\) | 39.8875 | 1.57916 | ||||||||
\(639\) | 14.4595 | 0.572010 | ||||||||
\(640\) | 41.1068 | 1.62489 | ||||||||
\(641\) | 1.83299 | 0.0723989 | 0.0361995 | − | 0.999345i | \(-0.488475\pi\) | ||||
0.0361995 | + | 0.999345i | \(0.488475\pi\) | |||||||
\(642\) | 120.260 | 4.74630 | ||||||||
\(643\) | 11.8871 | 0.468780 | 0.234390 | − | 0.972143i | \(-0.424691\pi\) | ||||
0.234390 | + | 0.972143i | \(0.424691\pi\) | |||||||
\(644\) | 163.605 | 6.44694 | ||||||||
\(645\) | −32.6007 | −1.28365 | ||||||||
\(646\) | −18.7212 | −0.736574 | ||||||||
\(647\) | 9.15698 | 0.359998 | 0.179999 | − | 0.983667i | \(-0.442391\pi\) | ||||
0.179999 | + | 0.983667i | \(0.442391\pi\) | |||||||
\(648\) | −32.3135 | −1.26939 | ||||||||
\(649\) | 1.12539 | 0.0441755 | ||||||||
\(650\) | −22.3249 | −0.875656 | ||||||||
\(651\) | 54.3567 | 2.13041 | ||||||||
\(652\) | 28.5589 | 1.11845 | ||||||||
\(653\) | 8.93522 | 0.349662 | 0.174831 | − | 0.984598i | \(-0.444062\pi\) | ||||
0.174831 | + | 0.984598i | \(0.444062\pi\) | |||||||
\(654\) | −52.6946 | −2.06052 | ||||||||
\(655\) | 2.19652 | 0.0858253 | ||||||||
\(656\) | 166.314 | 6.49346 | ||||||||
\(657\) | −14.3274 | −0.558964 | ||||||||
\(658\) | −35.6416 | −1.38945 | ||||||||
\(659\) | 49.3492 | 1.92237 | 0.961185 | − | 0.275904i | \(-0.0889773\pi\) | ||||
0.961185 | + | 0.275904i | \(0.0889773\pi\) | |||||||
\(660\) | −39.0867 | −1.52145 | ||||||||
\(661\) | −35.6402 | −1.38624 | −0.693121 | − | 0.720821i | \(-0.743765\pi\) | ||||
−0.693121 | + | 0.720821i | \(0.743765\pi\) | |||||||
\(662\) | 73.1810 | 2.84426 | ||||||||
\(663\) | 42.0199 | 1.63192 | ||||||||
\(664\) | −90.5714 | −3.51485 | ||||||||
\(665\) | 7.24535 | 0.280963 | ||||||||
\(666\) | −132.271 | −5.12540 | ||||||||
\(667\) | −66.3574 | −2.56937 | ||||||||
\(668\) | −22.7821 | −0.881466 | ||||||||
\(669\) | −35.4051 | −1.36884 | ||||||||
\(670\) | −14.2250 | −0.549561 | ||||||||
\(671\) | 6.15016 | 0.237424 | ||||||||
\(672\) | −215.380 | −8.30847 | ||||||||
\(673\) | 36.8833 | 1.42175 | 0.710873 | − | 0.703320i | \(-0.248300\pi\) | ||||
0.710873 | + | 0.703320i | \(0.248300\pi\) | |||||||
\(674\) | 0.773682 | 0.0298011 | ||||||||
\(675\) | 20.0839 | 0.773029 | ||||||||
\(676\) | −28.0291 | −1.07804 | ||||||||
\(677\) | −22.7248 | −0.873386 | −0.436693 | − | 0.899611i | \(-0.643850\pi\) | ||||
−0.436693 | + | 0.899611i | \(0.643850\pi\) | |||||||
\(678\) | 147.532 | 5.66594 | ||||||||
\(679\) | −39.1604 | −1.50284 | ||||||||
\(680\) | 67.5940 | 2.59211 | ||||||||
\(681\) | 4.74952 | 0.182002 | ||||||||
\(682\) | 23.5642 | 0.902320 | ||||||||
\(683\) | 27.6502 | 1.05801 | 0.529003 | − | 0.848620i | \(-0.322566\pi\) | ||||
0.529003 | + | 0.848620i | \(0.322566\pi\) | |||||||
\(684\) | 37.8107 | 1.44573 | ||||||||
\(685\) | −1.82676 | −0.0697968 | ||||||||
\(686\) | 7.20550 | 0.275107 | ||||||||
\(687\) | −38.9801 | −1.48718 | ||||||||
\(688\) | −109.462 | −4.17321 | ||||||||
\(689\) | −16.4801 | −0.627840 | ||||||||
\(690\) | 89.3654 | 3.40208 | ||||||||
\(691\) | 37.6609 | 1.43269 | 0.716344 | − | 0.697747i | \(-0.245814\pi\) | ||||
0.716344 | + | 0.697747i | \(0.245814\pi\) | |||||||
\(692\) | 53.6831 | 2.04072 | ||||||||
\(693\) | 36.3340 | 1.38022 | ||||||||
\(694\) | 33.9236 | 1.28772 | ||||||||
\(695\) | 15.0126 | 0.569459 | ||||||||
\(696\) | 217.446 | 8.24226 | ||||||||
\(697\) | 62.6565 | 2.37328 | ||||||||
\(698\) | 46.5184 | 1.76075 | ||||||||
\(699\) | 28.4460 | 1.07592 | ||||||||
\(700\) | 60.5955 | 2.29030 | ||||||||
\(701\) | 22.1947 | 0.838281 | 0.419141 | − | 0.907921i | \(-0.362331\pi\) | ||||
0.419141 | + | 0.907921i | \(0.362331\pi\) | |||||||
\(702\) | −51.2229 | −1.93329 | ||||||||
\(703\) | 12.0715 | 0.455285 | ||||||||
\(704\) | −44.2441 | −1.66751 | ||||||||
\(705\) | −14.1658 | −0.533516 | ||||||||
\(706\) | 80.9022 | 3.04479 | ||||||||
\(707\) | 57.9526 | 2.17953 | ||||||||
\(708\) | 9.80538 | 0.368509 | ||||||||
\(709\) | 30.7035 | 1.15309 | 0.576547 | − | 0.817064i | \(-0.304400\pi\) | ||||
0.576547 | + | 0.817064i | \(0.304400\pi\) | |||||||
\(710\) | 10.4655 | 0.392763 | ||||||||
\(711\) | 48.6203 | 1.82340 | ||||||||
\(712\) | 151.482 | 5.67703 | ||||||||
\(713\) | −39.2018 | −1.46812 | ||||||||
\(714\) | −156.745 | −5.86602 | ||||||||
\(715\) | −7.04988 | −0.263651 | ||||||||
\(716\) | −100.069 | −3.73976 | ||||||||
\(717\) | −34.7217 | −1.29670 | ||||||||
\(718\) | 12.7666 | 0.476446 | ||||||||
\(719\) | 3.56573 | 0.132979 | 0.0664897 | − | 0.997787i | \(-0.478820\pi\) | ||||
0.0664897 | + | 0.997787i | \(0.478820\pi\) | |||||||
\(720\) | −105.946 | −3.94839 | ||||||||
\(721\) | −9.96471 | −0.371105 | ||||||||
\(722\) | 46.7439 | 1.73963 | ||||||||
\(723\) | −35.0632 | −1.30401 | ||||||||
\(724\) | −122.129 | −4.53889 | ||||||||
\(725\) | −24.5772 | −0.912776 | ||||||||
\(726\) | −61.5454 | −2.28416 | ||||||||
\(727\) | 28.7650 | 1.06683 | 0.533417 | − | 0.845852i | \(-0.320908\pi\) | ||||
0.533417 | + | 0.845852i | \(0.320908\pi\) | |||||||
\(728\) | −96.6965 | −3.58381 | ||||||||
\(729\) | −39.7637 | −1.47273 | ||||||||
\(730\) | −10.3698 | −0.383805 | ||||||||
\(731\) | −41.2385 | −1.52526 | ||||||||
\(732\) | 53.5855 | 1.98058 | ||||||||
\(733\) | −13.3095 | −0.491596 | −0.245798 | − | 0.969321i | \(-0.579050\pi\) | ||||
−0.245798 | + | 0.969321i | \(0.579050\pi\) | |||||||
\(734\) | −18.0788 | −0.667301 | ||||||||
\(735\) | 31.7631 | 1.17160 | ||||||||
\(736\) | 155.331 | 5.72559 | ||||||||
\(737\) | 6.51034 | 0.239812 | ||||||||
\(738\) | −173.914 | −6.40188 | ||||||||
\(739\) | −19.2829 | −0.709333 | −0.354666 | − | 0.934993i | \(-0.615406\pi\) | ||||
−0.354666 | + | 0.934993i | \(0.615406\pi\) | |||||||
\(740\) | −69.6600 | −2.56075 | ||||||||
\(741\) | 10.6444 | 0.391031 | ||||||||
\(742\) | 61.4747 | 2.25681 | ||||||||
\(743\) | −2.19734 | −0.0806124 | −0.0403062 | − | 0.999187i | \(-0.512833\pi\) | ||||
−0.0403062 | + | 0.999187i | \(0.512833\pi\) | |||||||
\(744\) | 128.460 | 4.70956 | ||||||||
\(745\) | −15.5085 | −0.568188 | ||||||||
\(746\) | −48.7094 | −1.78338 | ||||||||
\(747\) | 53.4820 | 1.95680 | ||||||||
\(748\) | −49.4430 | −1.80782 | ||||||||
\(749\) | −58.8743 | −2.15122 | ||||||||
\(750\) | 89.0355 | 3.25112 | ||||||||
\(751\) | 49.0429 | 1.78960 | 0.894800 | − | 0.446468i | \(-0.147318\pi\) | ||||
0.894800 | + | 0.446468i | \(0.147318\pi\) | |||||||
\(752\) | −47.5641 | −1.73449 | ||||||||
\(753\) | −56.8860 | −2.07304 | ||||||||
\(754\) | 62.6830 | 2.28278 | ||||||||
\(755\) | 11.5330 | 0.419729 | ||||||||
\(756\) | 139.032 | 5.05654 | ||||||||
\(757\) | 8.64068 | 0.314051 | 0.157025 | − | 0.987595i | \(-0.449810\pi\) | ||||
0.157025 | + | 0.987595i | \(0.449810\pi\) | |||||||
\(758\) | 60.3965 | 2.19370 | ||||||||
\(759\) | −40.8997 | −1.48456 | ||||||||
\(760\) | 17.1228 | 0.621108 | ||||||||
\(761\) | 31.4275 | 1.13924 | 0.569622 | − | 0.821906i | \(-0.307089\pi\) | ||||
0.569622 | + | 0.821906i | \(0.307089\pi\) | |||||||
\(762\) | −82.4126 | −2.98549 | ||||||||
\(763\) | 25.7970 | 0.933913 | ||||||||
\(764\) | 59.6501 | 2.15806 | ||||||||
\(765\) | −39.9139 | −1.44309 | ||||||||
\(766\) | 65.0892 | 2.35177 | ||||||||
\(767\) | 1.76855 | 0.0638586 | ||||||||
\(768\) | −80.9777 | −2.92203 | ||||||||
\(769\) | −0.0262640 | −0.000947103 0 | −0.000473551 | − | 1.00000i | \(-0.500151\pi\) | ||||
−0.000473551 | 1.00000i | \(0.500151\pi\) | ||||||||
\(770\) | 26.2978 | 0.947707 | ||||||||
\(771\) | −60.4500 | −2.17705 | ||||||||
\(772\) | 34.1304 | 1.22838 | ||||||||
\(773\) | −38.3693 | −1.38005 | −0.690023 | − | 0.723787i | \(-0.742400\pi\) | ||||
−0.690023 | + | 0.723787i | \(0.742400\pi\) | |||||||
\(774\) | 114.465 | 4.11435 | ||||||||
\(775\) | −14.5194 | −0.521553 | ||||||||
\(776\) | −92.5469 | −3.32224 | ||||||||
\(777\) | 101.070 | 3.62586 | ||||||||
\(778\) | −66.0106 | −2.36660 | ||||||||
\(779\) | 15.8720 | 0.568674 | ||||||||
\(780\) | −61.4247 | −2.19936 | ||||||||
\(781\) | −4.78972 | −0.171390 | ||||||||
\(782\) | 113.043 | 4.04243 | ||||||||
\(783\) | −56.3907 | −2.01524 | ||||||||
\(784\) | 106.650 | 3.80892 | ||||||||
\(785\) | −33.8294 | −1.20742 | ||||||||
\(786\) | −12.0375 | −0.429362 | ||||||||
\(787\) | −48.5157 | −1.72940 | −0.864699 | − | 0.502290i | \(-0.832491\pi\) | ||||
−0.864699 | + | 0.502290i | \(0.832491\pi\) | |||||||
\(788\) | −70.2008 | −2.50080 | ||||||||
\(789\) | −67.3985 | −2.39945 | ||||||||
\(790\) | 35.1904 | 1.25202 | ||||||||
\(791\) | −72.2253 | −2.56804 | ||||||||
\(792\) | 85.8673 | 3.05116 | ||||||||
\(793\) | 9.66496 | 0.343213 | ||||||||
\(794\) | 50.4591 | 1.79073 | ||||||||
\(795\) | 24.4333 | 0.866559 | ||||||||
\(796\) | −42.5634 | −1.50862 | ||||||||
\(797\) | 16.5500 | 0.586231 | 0.293116 | − | 0.956077i | \(-0.405308\pi\) | ||||
0.293116 | + | 0.956077i | \(0.405308\pi\) | |||||||
\(798\) | −39.7062 | −1.40558 | ||||||||
\(799\) | −17.9192 | −0.633935 | ||||||||
\(800\) | 57.5311 | 2.03403 | ||||||||
\(801\) | −89.4494 | −3.16054 | ||||||||
\(802\) | 43.2706 | 1.52794 | ||||||||
\(803\) | 4.74594 | 0.167481 | ||||||||
\(804\) | 56.7237 | 2.00049 | ||||||||
\(805\) | −43.7494 | −1.54196 | ||||||||
\(806\) | 37.0311 | 1.30436 | ||||||||
\(807\) | −61.1643 | −2.15309 | ||||||||
\(808\) | 136.958 | 4.81817 | ||||||||
\(809\) | 22.4985 | 0.791005 | 0.395502 | − | 0.918465i | \(-0.370570\pi\) | ||||
0.395502 | + | 0.918465i | \(0.370570\pi\) | |||||||
\(810\) | 13.8104 | 0.485248 | ||||||||
\(811\) | −21.7528 | −0.763843 | −0.381921 | − | 0.924195i | \(-0.624737\pi\) | ||||
−0.381921 | + | 0.924195i | \(0.624737\pi\) | |||||||
\(812\) | −170.138 | −5.97066 | ||||||||
\(813\) | 47.5261 | 1.66681 | ||||||||
\(814\) | 43.8149 | 1.53571 | ||||||||
\(815\) | −7.63689 | −0.267509 | ||||||||
\(816\) | −209.178 | −7.32268 | ||||||||
\(817\) | −10.4464 | −0.365475 | ||||||||
\(818\) | −12.9503 | −0.452795 | ||||||||
\(819\) | 57.0988 | 1.99519 | ||||||||
\(820\) | −91.5913 | −3.19851 | ||||||||
\(821\) | −11.4291 | −0.398878 | −0.199439 | − | 0.979910i | \(-0.563912\pi\) | ||||
−0.199439 | + | 0.979910i | \(0.563912\pi\) | |||||||
\(822\) | 10.0111 | 0.349176 | ||||||||
\(823\) | 10.0768 | 0.351257 | 0.175628 | − | 0.984457i | \(-0.443804\pi\) | ||||
0.175628 | + | 0.984457i | \(0.443804\pi\) | |||||||
\(824\) | −23.5494 | −0.820381 | ||||||||
\(825\) | −15.1483 | −0.527396 | ||||||||
\(826\) | −6.59712 | −0.229543 | ||||||||
\(827\) | 5.79378 | 0.201470 | 0.100735 | − | 0.994913i | \(-0.467881\pi\) | ||||
0.100735 | + | 0.994913i | \(0.467881\pi\) | |||||||
\(828\) | −228.311 | −7.93437 | ||||||||
\(829\) | 8.17338 | 0.283873 | 0.141937 | − | 0.989876i | \(-0.454667\pi\) | ||||
0.141937 | + | 0.989876i | \(0.454667\pi\) | |||||||
\(830\) | 38.7091 | 1.34361 | ||||||||
\(831\) | 28.6806 | 0.994918 | ||||||||
\(832\) | −69.5294 | −2.41050 | ||||||||
\(833\) | 40.1790 | 1.39212 | ||||||||
\(834\) | −82.2723 | −2.84886 | ||||||||
\(835\) | 6.09213 | 0.210827 | ||||||||
\(836\) | −12.5248 | −0.433179 | ||||||||
\(837\) | −33.3138 | −1.15149 | ||||||||
\(838\) | −43.6795 | −1.50888 | ||||||||
\(839\) | −31.7323 | −1.09552 | −0.547760 | − | 0.836635i | \(-0.684519\pi\) | ||||
−0.547760 | + | 0.836635i | \(0.684519\pi\) | |||||||
\(840\) | 143.362 | 4.94645 | ||||||||
\(841\) | 40.0070 | 1.37955 | ||||||||
\(842\) | −3.95360 | −0.136250 | ||||||||
\(843\) | 75.6373 | 2.60509 | ||||||||
\(844\) | −57.1109 | −1.96584 | ||||||||
\(845\) | 7.49521 | 0.257843 | ||||||||
\(846\) | 49.7379 | 1.71002 | ||||||||
\(847\) | 30.1299 | 1.03528 | ||||||||
\(848\) | 82.0388 | 2.81722 | ||||||||
\(849\) | 73.2644 | 2.51443 | ||||||||
\(850\) | 41.8687 | 1.43608 | ||||||||
\(851\) | −72.8910 | −2.49867 | ||||||||
\(852\) | −41.7322 | −1.42972 | ||||||||
\(853\) | −38.3474 | −1.31299 | −0.656496 | − | 0.754330i | \(-0.727962\pi\) | ||||
−0.656496 | + | 0.754330i | \(0.727962\pi\) | |||||||
\(854\) | −36.0527 | −1.23370 | ||||||||
\(855\) | −10.1109 | −0.345785 | ||||||||
\(856\) | −139.136 | −4.75557 | ||||||||
\(857\) | −48.0678 | −1.64196 | −0.820982 | − | 0.570954i | \(-0.806574\pi\) | ||||
−0.820982 | + | 0.570954i | \(0.806574\pi\) | |||||||
\(858\) | 38.6350 | 1.31898 | ||||||||
\(859\) | 40.6676 | 1.38756 | 0.693780 | − | 0.720187i | \(-0.255944\pi\) | ||||
0.693780 | + | 0.720187i | \(0.255944\pi\) | |||||||
\(860\) | 60.2824 | 2.05561 | ||||||||
\(861\) | 132.890 | 4.52887 | ||||||||
\(862\) | 41.2607 | 1.40535 | ||||||||
\(863\) | −23.9701 | −0.815953 | −0.407977 | − | 0.912992i | \(-0.633766\pi\) | ||||
−0.407977 | + | 0.912992i | \(0.633766\pi\) | |||||||
\(864\) | 132.001 | 4.49076 | ||||||||
\(865\) | −14.3553 | −0.488095 | ||||||||
\(866\) | 68.3155 | 2.32145 | ||||||||
\(867\) | −29.6832 | −1.00810 | ||||||||
\(868\) | −100.512 | −3.41159 | ||||||||
\(869\) | −16.1055 | −0.546342 | ||||||||
\(870\) | −92.9336 | −3.15074 | ||||||||
\(871\) | 10.2310 | 0.346664 | ||||||||
\(872\) | 60.9654 | 2.06455 | ||||||||
\(873\) | 54.6485 | 1.84957 | ||||||||
\(874\) | 28.6359 | 0.968624 | ||||||||
\(875\) | −43.5879 | −1.47354 | ||||||||
\(876\) | 41.3508 | 1.39711 | ||||||||
\(877\) | 14.0601 | 0.474777 | 0.237388 | − | 0.971415i | \(-0.423709\pi\) | ||||
0.237388 | + | 0.971415i | \(0.423709\pi\) | |||||||
\(878\) | 35.2842 | 1.19078 | ||||||||
\(879\) | −12.9821 | −0.437875 | ||||||||
\(880\) | 35.0948 | 1.18304 | ||||||||
\(881\) | −26.0723 | −0.878398 | −0.439199 | − | 0.898390i | \(-0.644738\pi\) | ||||
−0.439199 | + | 0.898390i | \(0.644738\pi\) | |||||||
\(882\) | −111.524 | −3.75521 | ||||||||
\(883\) | −11.0266 | −0.371074 | −0.185537 | − | 0.982637i | \(-0.559402\pi\) | ||||
−0.185537 | + | 0.982637i | \(0.559402\pi\) | |||||||
\(884\) | −77.6996 | −2.61332 | ||||||||
\(885\) | −2.62204 | −0.0881390 | ||||||||
\(886\) | −23.5500 | −0.791177 | ||||||||
\(887\) | 13.2068 | 0.443440 | 0.221720 | − | 0.975110i | \(-0.428833\pi\) | ||||
0.221720 | + | 0.975110i | \(0.428833\pi\) | |||||||
\(888\) | 238.856 | 8.01547 | ||||||||
\(889\) | 40.3456 | 1.35315 | ||||||||
\(890\) | −64.7415 | −2.17014 | ||||||||
\(891\) | −6.32058 | −0.211747 | ||||||||
\(892\) | 65.4681 | 2.19203 | ||||||||
\(893\) | −4.53925 | −0.151900 | ||||||||
\(894\) | 84.9903 | 2.84250 | ||||||||
\(895\) | 26.7594 | 0.894467 | ||||||||
\(896\) | 110.285 | 3.68435 | ||||||||
\(897\) | −64.2737 | −2.14604 | ||||||||
\(898\) | 16.6461 | 0.555488 | ||||||||
\(899\) | 40.7670 | 1.35966 | ||||||||
\(900\) | −84.5612 | −2.81871 | ||||||||
\(901\) | 30.9070 | 1.02966 | ||||||||
\(902\) | 57.6092 | 1.91818 | ||||||||
\(903\) | −87.4638 | −2.91061 | ||||||||
\(904\) | −170.688 | −5.67701 | ||||||||
\(905\) | 32.6584 | 1.08560 | ||||||||
\(906\) | −63.2035 | −2.09980 | ||||||||
\(907\) | 9.09509 | 0.301998 | 0.150999 | − | 0.988534i | \(-0.451751\pi\) | ||||
0.150999 | + | 0.988534i | \(0.451751\pi\) | |||||||
\(908\) | −8.78241 | −0.291454 | ||||||||
\(909\) | −80.8730 | −2.68239 | ||||||||
\(910\) | 41.3269 | 1.36997 | ||||||||
\(911\) | 44.2686 | 1.46668 | 0.733342 | − | 0.679859i | \(-0.237959\pi\) | ||||
0.733342 | + | 0.679859i | \(0.237959\pi\) | |||||||
\(912\) | −52.9884 | −1.75462 | ||||||||
\(913\) | −17.7159 | −0.586311 | ||||||||
\(914\) | 15.3102 | 0.506418 | ||||||||
\(915\) | −14.3292 | −0.473710 | ||||||||
\(916\) | 72.0786 | 2.38154 | ||||||||
\(917\) | 5.89302 | 0.194605 | ||||||||
\(918\) | 96.0646 | 3.17060 | ||||||||
\(919\) | 53.1699 | 1.75391 | 0.876957 | − | 0.480569i | \(-0.159570\pi\) | ||||
0.876957 | + | 0.480569i | \(0.159570\pi\) | |||||||
\(920\) | −103.392 | −3.40873 | ||||||||
\(921\) | 15.6767 | 0.516565 | ||||||||
\(922\) | 94.6646 | 3.11761 | ||||||||
\(923\) | −7.52703 | −0.247755 | ||||||||
\(924\) | −104.865 | −3.44981 | ||||||||
\(925\) | −26.9971 | −0.887661 | ||||||||
\(926\) | 13.8204 | 0.454166 | ||||||||
\(927\) | 13.9058 | 0.456726 | ||||||||
\(928\) | −161.533 | −5.30259 | ||||||||
\(929\) | −17.3158 | −0.568112 | −0.284056 | − | 0.958808i | \(-0.591680\pi\) | ||||
−0.284056 | + | 0.958808i | \(0.591680\pi\) | |||||||
\(930\) | −54.9021 | −1.80031 | ||||||||
\(931\) | 10.1780 | 0.333572 | ||||||||
\(932\) | −52.5998 | −1.72296 | ||||||||
\(933\) | 68.5659 | 2.24475 | ||||||||
\(934\) | −50.6761 | −1.65817 | ||||||||
\(935\) | 13.2215 | 0.432389 | ||||||||
\(936\) | 134.940 | 4.41066 | ||||||||
\(937\) | −27.4506 | −0.896771 | −0.448386 | − | 0.893840i | \(-0.648001\pi\) | ||||
−0.448386 | + | 0.893840i | \(0.648001\pi\) | |||||||
\(938\) | −38.1641 | −1.24610 | ||||||||
\(939\) | 60.2558 | 1.96637 | ||||||||
\(940\) | 26.1942 | 0.854362 | ||||||||
\(941\) | 15.1633 | 0.494310 | 0.247155 | − | 0.968976i | \(-0.420504\pi\) | ||||
0.247155 | + | 0.968976i | \(0.420504\pi\) | |||||||
\(942\) | 185.393 | 6.04042 | ||||||||
\(943\) | −95.8395 | −3.12096 | ||||||||
\(944\) | −8.80394 | −0.286544 | ||||||||
\(945\) | −37.1783 | −1.20941 | ||||||||
\(946\) | −37.9165 | −1.23277 | ||||||||
\(947\) | 23.2061 | 0.754098 | 0.377049 | − | 0.926193i | \(-0.376939\pi\) | ||||
0.377049 | + | 0.926193i | \(0.376939\pi\) | |||||||
\(948\) | −140.325 | −4.55755 | ||||||||
\(949\) | 7.45823 | 0.242105 | ||||||||
\(950\) | 10.6061 | 0.344107 | ||||||||
\(951\) | 80.9130 | 2.62378 | ||||||||
\(952\) | 181.347 | 5.87748 | ||||||||
\(953\) | 20.3035 | 0.657695 | 0.328847 | − | 0.944383i | \(-0.393340\pi\) | ||||
0.328847 | + | 0.944383i | \(0.393340\pi\) | |||||||
\(954\) | −85.7881 | −2.77749 | ||||||||
\(955\) | −15.9509 | −0.516160 | ||||||||
\(956\) | 64.2044 | 2.07652 | ||||||||
\(957\) | 42.5327 | 1.37489 | ||||||||
\(958\) | −87.0907 | −2.81377 | ||||||||
\(959\) | −4.90098 | −0.158261 | ||||||||
\(960\) | 103.084 | 3.32702 | ||||||||
\(961\) | −6.91617 | −0.223102 | ||||||||
\(962\) | 68.8549 | 2.21997 | ||||||||
\(963\) | 82.1592 | 2.64754 | ||||||||
\(964\) | 64.8359 | 2.08822 | ||||||||
\(965\) | −9.12676 | −0.293801 | ||||||||
\(966\) | 239.757 | 7.71405 | ||||||||
\(967\) | 21.7092 | 0.698121 | 0.349061 | − | 0.937100i | \(-0.386501\pi\) | ||||
0.349061 | + | 0.937100i | \(0.386501\pi\) | |||||||
\(968\) | 71.2053 | 2.28862 | ||||||||
\(969\) | −19.9627 | −0.641294 | ||||||||
\(970\) | 39.5534 | 1.26998 | ||||||||
\(971\) | −2.33267 | −0.0748590 | −0.0374295 | − | 0.999299i | \(-0.511917\pi\) | ||||
−0.0374295 | + | 0.999299i | \(0.511917\pi\) | |||||||
\(972\) | 53.7401 | 1.72371 | ||||||||
\(973\) | 40.2769 | 1.29122 | ||||||||
\(974\) | 96.9145 | 3.10534 | ||||||||
\(975\) | −23.8055 | −0.762386 | ||||||||
\(976\) | −48.1128 | −1.54005 | ||||||||
\(977\) | 45.6936 | 1.46187 | 0.730933 | − | 0.682449i | \(-0.239085\pi\) | ||||
0.730933 | + | 0.682449i | \(0.239085\pi\) | |||||||
\(978\) | 41.8519 | 1.33828 | ||||||||
\(979\) | 29.6301 | 0.946983 | ||||||||
\(980\) | −58.7336 | −1.87618 | ||||||||
\(981\) | −35.9997 | −1.14938 | ||||||||
\(982\) | −72.1712 | −2.30307 | ||||||||
\(983\) | −15.4750 | −0.493574 | −0.246787 | − | 0.969070i | \(-0.579375\pi\) | ||||
−0.246787 | + | 0.969070i | \(0.579375\pi\) | |||||||
\(984\) | 314.055 | 10.0117 | ||||||||
\(985\) | 18.7723 | 0.598135 | ||||||||
\(986\) | −117.557 | −3.74378 | ||||||||
\(987\) | −38.0052 | −1.20972 | ||||||||
\(988\) | −19.6827 | −0.626190 | ||||||||
\(989\) | 63.0785 | 2.00578 | ||||||||
\(990\) | −36.6986 | −1.16636 | ||||||||
\(991\) | 37.3148 | 1.18534 | 0.592672 | − | 0.805444i | \(-0.298073\pi\) | ||||
0.592672 | + | 0.805444i | \(0.298073\pi\) | |||||||
\(992\) | −95.4286 | −3.02986 | ||||||||
\(993\) | 78.0342 | 2.47634 | ||||||||
\(994\) | 28.0777 | 0.890570 | ||||||||
\(995\) | 11.3818 | 0.360828 | ||||||||
\(996\) | −154.356 | −4.89097 | ||||||||
\(997\) | −21.0858 | −0.667792 | −0.333896 | − | 0.942610i | \(-0.608364\pi\) | ||||
−0.333896 | + | 0.942610i | \(0.608364\pi\) | |||||||
\(998\) | 31.9117 | 1.01015 | ||||||||
\(999\) | −61.9430 | −1.95979 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8011.2.a.b.1.5 | ✓ | 358 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8011.2.a.b.1.5 | ✓ | 358 | 1.1 | even | 1 | trivial |